Does the country which your masters came from matter for university teaching?

Hello, I'm currently on the JET program and I'm thinking of what to do post JET. I'm leaning towards going to graduate school as I would like to teach English at a university.

I would like to study a Japanese university, but then I realized in terms of TESL are universities looking for master degrees attained abroad? I'm from the US and already have my bachelor's in TESL.

If anyone with experience in university teaching has any input, thanks!